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This paper proposes a novel probabilistic approach for multidisciplinary design optimization (MDO) under uncertainty, especially for systems with feedback coupled analyses with multiple coupling variables. The proposed approach consists of four components: multidisciplinary analysis, Bayesian network, copula-based sampling, and design optimization. The Bayesian network represents the joint distribution of multiple variables through marginal distributions and conditional probabilities, and updates the distributions based on new data. In this methodology, the Bayesian network is pursued in two directions: (1) probabilistic surrogate modeling to estimate the output uncertainty given values of the design variables, and (2) probabilistic multidisciplinary analysis (MDA) to infer the distributions of the coupling and output variables that satisfy interdisciplinary compatibility conditions. A copula-based sampling technique is employed for efficient sampling from the joint and conditional distributions. The proposed MDO methodology is implemented within a framework of reliability-based design optimization. The proposed Bayesian network surrogate model and copula sampling are used for efficient reliability assessment within the optimization framework. A mathematical example and an aeroelastic aircraft wing design are used to demonstrate the proposed probabilistic MDO methodology